Question

in the diagram below, ( overline{ad} parallel overline{eg} ), ( mangle bfc = 70^{circ} ) and ( mangle efb = 44^{circ} ). find ( mangle fcd ).

Explanation:

Step1: Find \(m\angle GFC\)

Since \(\angle EFB = 44^{\circ}\) and \(\angle BFC=70^{\circ}\), and \(\angle GFE = 180^{\circ}\) (straight - angle), then \(m\angle GFC=180^{\circ}-m\angle BFC - m\angle EFB\).

$$m\angle GFC=180^{\circ}-70^{\circ}-44^{\circ}=66^{\circ}$$

Step2: Use the property of parallel lines

Because \(\overline{AD}\parallel\overline{EG}\), and \(FC\) is a transversal. By the alternate - interior angles theorem (if two parallel lines are cut by a transversal, then alternate - interior angles are equal), \(m\angle FCD=m\angle GFC\)

Answer:

\(66^{\circ}\)